We have mapped the gaseous kinematics and the emission-line flux distributions and ratios from the inner \approx 680 pc radius of the Seyfert 1 galaxy Mrk 79 , using two-dimensional ( 2D ) near-IR J - and K _ { l } - band spectra obtained with the Gemini instrument NIFS at a spatial resolution of \approx 100 pc and velocity resolution of \approx 40 km s ^ { -1 } . The molecular hydrogen H _ { 2 } flux distribution presents two spiral arms extending by \approx 700 pc , one to the north and another to the south of the nucleus , with an excitation indicating heating by X-rays from the central source . The low velocity dispersion ( \sigma \approx 50 km s ^ { -1 } ) and rotation pattern supports a location of the H _ { 2 } gas in the disk of the galaxy . Blueshifts observed along the spiral arm in the far side of the galaxy and redshifts in the spiral arm in the near side , suggest that the spiral arms are feeding channels of H _ { 2 } to the inner 200 pc . From channel maps along the H _ { 2 } \lambda 2.1218 \mu m emission-line profile we estimate a mass inflow rate of \dot { M } _ { H _ { 2 } } \approx 4 \times 10 ^ { -3 } { M _ { \odot } yr ^ { -1 } } , which is one order of magnitude smaller than the mass accretion rate necessary to power the AGN of Mrk 79.The emission from the ionized gas ( traced by Pa \beta and [ Fe ii ] \lambda 1.2570 \mu m emission lines ) is correlated with the radio jet and with the narrow-band [ O iii ] flux distribution . Its kinematics shows both rotation and outflows to the north and south of the nucleus . The ionized gas mass outflow rate through a cross section with radius \approx 320 pc located at a distance of \approx 455 pc from the nucleus is \dot { M } _ { out } \approx 3.5 ~ { } { M _ { \odot } yr ^ { -1 } } , which is much larger than the AGN mass accretion rate , indicating that most of the outflowing gas originates in the interstellar medium surrounding the galaxy nucleus , which is pushed away by a nuclear jet .